Harlequins director of rugby, Conor O'Shea, may get a call from the Irish RFU to take over as head coach. Photograph: Tom Shaw/Getty Images

Harlequins can expect a call from the Irish Rugby Football Union before the end of the season if, as is becoming increasingly likely, the governing body finds itself looking for a national head coach to replace Declan Kidney, who faced calls for his resignation after Sunday's surprise defeat by Scotland.

Kidney's contract runs out at the end of the Six Nations and bookmakers in Ireland have long odds on his four-year reign being extended.

Conor O'Shea, the director of rugby at the Premiership champions Harlequins, is the favourite to take over, ahead of the Leinster coach, Joe Schmidt and the former Wales coach, Mike Ruddock, who is in charge of Ireland at Under-20 level and the All Ireland League leaders Lansdowne.

Ireland won the grand slam in 2009, Kidney's first season in charge, but since then they have won only half of their 18 matches in the tournament. They lost to Wales in the 2011 World Cup quarter-final and shipped 60 points against New Zealand in Hamilton last June, but their defeat at Murrayfield is being regarded as the ultimate indignity given that Kidney's men enjoyed 77% of possession.

"I think it is the beginning of the end for Declan," said the former Ireland and Lions outside-half, Tony Ward. "I do not say that lightly because I have the highest regard for him: in an era when most coaches get up your nose with their superiority complexes, he is a shining example of integrity, honesty, humility and complete lack of ego.

"I just think that four years is the shelf life for an international coach. Declan has got a few things wrong this Six Nations, such as taking the captaincy off Brian O'Driscoll and picking Paddy Jackson at outside-half in Scotland, even if the decisions were made for the right reasons. I do not see the RFU sacking him after the Six Nations, nor should they, but I think he will decide to step down."

Ward said O'Shea would be his choice as successor. The former Ireland full-back, who has helped turn Quins into a major force in the European game, is contracted at the Stoop until the end of next season. He was a panellist for RTE on Sunday when his two colleagues, George Hook and Brent Pope, called time on Kidney, the former saying he should be sacked immediately.

O'Shea demurred, saying: "As a coach, I know what Declan is going through and can put context into it. The team in Scotland was missing a number of players and at full strength we would have won the game. As it was, we gave a sucker an even chance having had them on toast. Declan is the most decorated coach we have ever had in Ireland and you need to sit down with the players before making any decision."

Kidney said after the 12-8 loss to Scotland, which followed a six-point home defeat to England, that he would "take a good look at myself" and the full-back Rob Kearney said everyone involved had to accept responsibility.

Ireland looked like title challengers after their opening day win in Wales, but their priority against France next week is to avoid wooden spoon contention.

"The defeat on Sunday almost defied rugby," said Ward. "We were so dominant. I was disappointed with the leadership because [Jamie] Heaslip opted not to give Jackson an early kick at goal to settle his nerves but went for a line-out that did not work and then, from a more difficult angle and with Scotland a prop light, he opted for the posts.

"Conor would be my choice to take Ireland forward. He has the track record, he trusts the people around him and he is Irish at a time when all our provinces are coached by New Zealanders. Schmidt and Ruddock are men of substances and strong candidates, while there will always be a place in the game for Declan."